Turbulence

Liquids and gases flow, hence they are known as fluids. Common examples of fluids are water and air. It is often noticed that when the water tap is turned on slightly, the stream that comes out is smooth and clear, but when it is turned on further, the stream becomes sinuous and there is no steady flow pattern. These are two kinds of flows. When the fluid speed is slow, the flow is steady and laminar. When it is fast, the flow becomes irregular and erratic. The latter is known as turbulence.

Turbulence is the rule rather than exception. Most fluid flows in nature and in engineering applications are turbulent. Hence turbulence is a problem of practical interest. A solid grasp of this ubiquitous phenomenon will, for example, allow engineers to reduce the drag on automobiles or airplanes, and, as a result, save fuel or enhance the mixing of fuel and oxidizer in combustion engines, subsequently producing cleaner and more efficient combustion.

Turbulence also poses challenging and profound questions for physics. How can such complex and chaotic behaviour occur when the physical laws that govern fluid motion are simple and well defined? How can we completely and accurately describe in quantitative terms the properties of turbulent flows? In fact fluid motion equations were derived in the 19th century, and scientists have been studying turbulence since the last century. Yet today, in the 21st century, it still remains a great challenge in physics.

In turbulent flows, the physical quantities of interest, such as velocity, pressure, and temperature, display irregular and complex temporal and spatial fluctuations. A key issue in fundamental studies of turbulence is to make sense of these complex fluctuations. However, it is highly difficult to derive quantitative results for probability distribution of a turbulent quantity from the equations of fluid motion.

One feature of turbulence is that it is composed of eddies or vortices. Large vortices continually break up into small ones, which in turn break up into even smaller ones, until the effect of fluid viscosity dissipates the kinetic energy of the smallest vortices into heat. Lewis Richardson described this process in a well-circulated verse:

In 1941, Andrei Kolmogorov translated, using mathematical language, this picture of energy transfer from large-scale motion to small-scale motion into a theory. Although his predictions have not been completely borne out by experiments, Kolmogorov's ideas have dominated turbulence research for more than 50 years. The deviations are believed to be associated with the uneven distribution of turbulent activity. Therefore, another major focus in turbulence research is to try to understand this intermittent nature of turbulence, that is, to solve the so-called intermittency problem.

Prof. Emily S.C. Ching obtained her B.Sc. from the University of Hong Kong in 1986 and her M.Phil. from The Chinese University of Hong Kong in 1988. She then went abroad to the United States where she received her Ph.D. from the University of Chicago in 1992. After doing post-doctoral work in the Institute for Theoretical Physics at the University of California, Santa Barbara, she joined The Chinese University of Hong Kong as lecturer in 1995. In recognition of her contributions to the understanding of the complex fluctuations in turbulence, Prof. Ching was awarded the 1999 Achievement in Asia Award by the Overseas Physics Association. Prof. Ching is a theoretical physicist and her research interests are non-equilibrium nonlinear systems, in particular, fluid turbulence and fracture dynamics.

Research Results

Prof. Emily S.C. Ching of the Department of Physics has been doing theoretical research work on turbulence since 1990. She was awarded a grant from the Research Grants Council (RGC) in 1995 for her first project at the University. The project, an extension of her doctoral work¹, gave rise to a framework for studying turbulence using conditional statistics². Using this approach, the probability distribution of any physical quantity of interest (such as velocity, pressure, and temperature) is obtained exactly in terms of two conditional averages, which are taken upon satisfaction of specific conditions. This framework has attracted a lot of interest, and has been extensively applied in the analyses of turbulent experiments. Interesting general features of different turbulent flows have since been discovered, and the deviation of the probability distribution of temperature fluctuations in thermal convection from a Gaussian has been understood. Recently, this framework has also found applications in other systems such as in the analysis of the Hang Seng Index.

Scientists generally believe that understanding of the intermittent nature of turbulence can be gained by studying the properties of a contaminant or pollutant that is carried by a turbulent flow. They found that one conditional average of the form studied extensively in Prof. Ching's framework plays a crucial role. This generated even greater interest in Prof. Ching's work, and led, in particular, to the research collaboration between her and Dr. Robert H. Kraichnan. Dr. Kraichnan is a world-renowned physicist who has studied turbulence for more than 40 years and been awarded various awards and prizes. The duo were able to obtain exact results for some conditional averages directly from the equations of fluid motion in certain turbulent flows³. Prof. Ching has further proposed that the intermittent nature of the pollutant concentration in one particular model is the sole result of the variations of the pollutant's local dissipation rate. Using this hypothesis, she obtained some quantitative results⁴.

Reference

Emily S.C. Ching, Phys. Rev. Lett., 70, 283 (1993); S.B. Pope and Emily S.C. Ching, Phys. Fluids, A5, 1529 (1993).
Emily S.C. Ching, Phys. Rev., E53, 5899 (1996).
Emily S.C. Ching and Robert H. Kraichnan, J. Stat. Phys., 93, 787 (1998).
Emily S.C. Ching, Phys. Rev. Lett., 79, 3644 (1997).
Emily S.C. Ching, Phys. Rev., E61, R33 (2000).

Prof. Ching's first project at the University was completed in early 1998. It answered some questions but raised even more. In August 1998, she was awarded funding from the RGC to embark on a second and ongoing project. The objective of this project is to test her hypothesis on the intermittent nature of the pollutant concentration, and to study the intermittency problem of temperature fluctuations in thermal convection.


	Figure 1 The black line represents the statistical properties of the temperature fluctuations in thermal convection under a buoyancy-dominated regime, while the red line represents that under an inertia-dominated regime.

The physical essence of the hypothesis receives support from the numerical data obtained from simulation of the model but the exact mathematical form proposed turns out to be invalid. In thermal convection, a temperature difference is applied across a closed box of fluid. Hot fluid rises and cold fluid falls. As a result, the fluid is driven into motion by the applied temperature difference. Thus, temperature in thermal convection is known as an active scalar, in contrast to a pollutant that is just carried by the flow. The problem of active scalar is richer and thus more interesting. Prof. Ching's results indicate that the temperature fluctuations in thermal convection have different statistical properties under different regimes⁵ (Figure 1).

In November 2000, Prof. Ching launched a third project, again with funding from the RGC. The focus this time is to study the relation between the velocity and the temperature fluctuations in thermal convection. Currently, there is no consensus among scientists on the interplay between velocity and temperature, and it is expected that this project can help to resolve the situation. Prof. Ching said, 'Turbulence is a huge challenge. But I believe light will be thrown on this intriguing phenomenon slowly through hard work.'